Ordered Pairs, Intercepts, And Slopes Worksheet Page 5
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18Secton . — Ordered Pars, Intercepts, and Slopes
3
Find the Slope of a Linear Equation
1. Find two ordered pair solutions to the equation (use Technique 1).
2. Substitute the ordered pair values into the Slope Formula to determine the slope.
3. Validate by finding a third ordered pair solution to the equation and using this point
(together with one of the previous two ordered pair solutions) to recalculate the
slope.
►
Example 3: Find the slope for the equation 2x + 3y = 10.
(
y
–
y
)
Use the values previously calculated from Example 1:
m=
2
1
(
x
–
x
)
2
1
(–4, 6) and (8, –2)
(–2 – 6)
m=
(8 –(–4))
(–8)
m=
(12)
2
slope
= –
3
2 +3 =10
x
y
Validate:
Choose a value for x: Let x = 2
2(2)+3 =10
y
4+3 =10
y
4 – 4+3 =10 – 4
y
3 = 6
y
y
= 2
An ordered pair solution is: (2, 2).
(
y
–
y
)
2
1
Let (2, 2) be P
and use (–4, 6) as
m=
1
(
x
–
x
)
P
. Substitute the values into the
2
1
2
Slope Formula:
(6 –2)
m=
(–4 –2)
(4)
m=
(–6)
2
slope
= –
3
We can rearrange the original equation
2
x
+
3
y
=
10
(2x + 3y = 10) into slope-intercept form and
-
2
x
+
2
x
+
3
y
=
10 2
-
x
visually check the slope and y-intercept:
y
= -
x
+
3
2
10
3
y
-
2
x
10
=
+
3
3
3
y = m x + b
2
10
y
= -
x
+
2
10
3
3
y
= –
x
+
3
3
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